A method to reconstruct and apply 3D primary fluence for treatment delivery verification

Abstract Motivation In this study, a method is reported to perform IMRT and VMAT treatment delivery verification using 3D volumetric primary beam fluences reconstructed directly from planned beam parameters and treatment delivery records. The goals of this paper are to demonstrate that 1) 3D beam fluences can be reconstructed efficiently, 2) quality assurance (QA) based on the reconstructed 3D fluences is capable of detecting additional treatment delivery errors, particularly for VMAT plans, beyond those identifiable by other existing treatment delivery verification methods, and 3) QA results based on 3D fluence calculation (3DFC) are correlated with QA results based on physical phantom measurements and radiation dose recalculations. Methods Using beam parameters extracted from DICOM plan files and treatment delivery log files, 3D volumetric primary fluences are reconstructed by forward‐projecting the beam apertures, defined by the MLC leaf positions and modulated by beam MU values, at all gantry angles using first‐order ray tracing. Treatment delivery verifications are performed by comparing 3D fluences reconstructed using beam parameters in delivery log files against those reconstructed from treatment plans. Passing rates are then determined using both voxel intensity differences and a 3D gamma analysis. QA sensitivity to various sources of errors is defined as the observed differences in passing rates. Correlations between passing rates obtained from QA derived from both 3D fluence calculations and physical measurements are investigated prospectively using 20 clinical treatment plans with artificially introduced machine delivery errors. Results Studies with artificially introduced errors show that common treatment delivery problems including gantry angle errors, MU errors, jaw position errors, collimator rotation errors, and MLC leaf position errors were detectable at less than normal machine tolerances. The reported 3DFC QA method has greater sensitivity than measurement‐based QA methods. Statistical analysis‐based Spearman's correlations shows that the 3DFC QA passing rates are significantly correlated with passing rates of physical phantom measurement‐based QA methods. Conclusion Among measurement‐less treatment delivery verification methods, the reported 3DFC method is less demanding than those based on full dose re‐calculations, and more comprehensive than those that solely checks beam parameters in treatment log files. With QA passing rates correlating to measurement‐based passing rates, the 3DFC QA results could be useful for complementing the physical phantom measurements, or verifying treatment deliveries when physical measurements are not available. For the past 4+ years, the reported method has been implemented at authors’ institution 1) as a complementary metric to physical phantom measurements for pretreatment, patient‐specific QA of IMRT and VMAT plans, and 2) as an important part of the log file‐based automated verification of daily patient treatment deliveries. It has been demonstrated to be useful in catching both treatment plan data transfer errors and treatment delivery problems.

Conclusion: Among measurement-less treatment delivery verification methods, the reported 3DFC method is less demanding than those based on full dose re-calculations, and more comprehensive than those that solely checks beam parameters in treatment log files. With QA passing rates correlating to measurement-based passing rates, the 3DFC QA results could be useful for complementing the physical phantom measurements, or verifying treatment deliveries when physical measurements are not available. For the past 4+ years, the reported method has been implemented at authors' institution 1) as a complementary metric to physical phantom measurements for pretreatment, patient-specific QA of IMRT and VMAT plans, and 2) as an important part of the log file-based automated verification of daily patient treatment deliveries. It has been demonstrated to be useful in catching both treatment plan data transfer errors and treatment delivery problems.

| INTRODUCTION
In intensity-modulated radiotherapy (IMRT) 1 and volumetric-modulated arc therapy (VMAT), 2 radiation is delivered in many individual beam apertures of varying intensities to achieve highly conformal dose distributions to the planning target volume (PTV), that minimize dose to nearby health tissues. 3 During delivery, mechanical parameters (e.g., MU, dose rate, gantry angle, collimator angle, jaw position and MLC leaf positions) are synchronized to planned values, specified by control points (CP). 4 Given the complexity of these treatments, quality assurance (QA) for treatment delivery is essential in detecting various types of delivery failures in order to ensure the accuracy of a patient's dosimetry and safety. IMRT/VMAT QA can be performed using point dose and planar dose measurements obtained via physical phantoms, 2D beam fluences, and dose recalculations based on machine delivery log files. [4][5][6] In comparison to conventional measurement-based QA, QA using log files offers various advantages including sampling higher spatial and temporal resolutions, not requiring measurement devices or phantoms, providing QA for fractional deliveries to patients, and being readily automated. 5,6 Performing IMRT QA using log files has been claimed to be more effective and efficient than, and complementary to, physical dose measurement-based QA. [7][8][9][10][11][12] A major, ongoing debate in the medical physics community is whether IMRT QA using log files can replace conventional measurement-based methods. 5 Numerous reports on using log files for IMRT/VMAT QA have been presented in literature. [13][14][15][16][17][18] Logged beam parameters can be compared to planned values based on a relatively simple value-tovalue comparison. Dose recalculations that incorporate parameters recorded in log files can verify the accuracy of delivered dose. Computation time has been significantly reduced with GPU acceleration; [19][20][21][22][23] however, comparing dose distributions can be complicated by differences in dose calculation engines and treatment planning systems (TPS), the accuracy of electron density determined in the daily patient localization cone-beam CT images, and other factors.
Traditionally in IMRT QA, verification of delivered 2D fluence maps for individual beams has been widely used. 8  2D fluence can also be digitally and proximately reconstructed from treatment plan parameters or LINAC machine log files by integrating across a beam aperture multiplied by the per-segment beam MU. 10,[26][27][28] At the authors' institution, 2D beam fluences digitally reconstructed from the DICOM plans and treatment delivery log files have enabled detection of many errors for IMRT plans, including human operating mistakes (resulting in wrong plans, wrong beams, or wrong beam parameters), flawed and suboptimal treatment plans (containing undeliverable or incorrect machine parameters), data transfer problems (resulting from unintended parameter changes), and other minor false positive errors. 11 However, for the case of VMAT QA, such 2D beam fluence verification per beam angle may not be appropriate because instantaneous beam aperture errors for VMAT deliveries were significant (up to 15%) for highly modulated plans even though MLC leaves were well-within tolerances. 29 A composite 2D fluence for a VMAT beam at a fixed gantry angle could be computed, 30 but error detection using such fluence is suboptimal due to the ignored gantry rotation. We therefore were motivated to develop an alternative 3D fluence calculation QA method, i.e., 3DFC, that (1) could be more sensitive to detect certain delivery machine errors (such as gantry rotation errors), (2) could provide enhanced visualization of beam delivery discrepancies respective to LIU ET AL.
| 129 the tumor target geometry, and (3) could infer correlations between random treatment delivery discrepancies to dose discrepancies.
In this study, a simple and efficient QA method based on 3D fluence calculation is reported. This method enables rapid calculation of 3D fluences using beam parameters from machine log files and DICOM plan files. Our goal is not to replace traditional physical phantom measurement-based QA or a full-scale dose calculation, but rather to present a simpler, complimentary solution for detecting potential delivery machine parameters errors and plan parameter transfer errors with improved 3D visualization. The reported 3DFC QA method mainly focuses on checking delivery errors of machine parametersinstead of scrutinizing TPS commissioning errorswhile potentially improving error sensitivities comparing to the traditional QA methods. Toward this goal, we examine correlations between the resultant passing rates from our reported 3DFC QA and conventional measurement-based QA in detail.

| Data
To calculate and verify the 3D fluence volume, both the planned beam parameters from DICOM plans and the reported beam parameters from the beam delivery log files are used. Beam parameters are defined similarly in the DICOM plans and machine log files. In To be concise, only the TrueBeam trajectory log files and VMAT plans will be discussed in the following sections.

| 3D fluence calculation (3DFC)
Two-dimensional beam fluence can be digitally computed based from machine log files by integrating the per-segment beam aperture multiplied by the per-segment beam MU. 10 In contrast, the 3D volumetric fluence is calculated by forward-projecting beam apertures, modulated by beam monitor units (MU), at all beam angles. In this paper, 2D and 3D fluence calculation methods are referred to as 2DFC and 3DFC, respectively, and IMRT and VMAT delivery QA using 2DFC and 3DFC methods are referred to as 2DFC QA and 3DFC QA, respectively.
Consider a point r 2 X, where Ω is the target 3D fluence volume around the beam isocenter. x, y and z represent coordinates of the point r with the origin defined at the beam isocenter, the 3D fluence intensity IðrÞ is calculated, using the beam parameters in the machine log files, as: where t is the delivery time, F is the 2D beam intensity profile in air, _ D is the dose rate in MU/s, SAD is the source-to-axis distance, sðtÞ is the source position, and M is the beam aperture mask with M = 1 if r 0 is inside the beam aperture or M = 0 otherwise. IðrÞ represents the total MU delivered to the point r by the cumulative beam aperture the entire beam delivery. It is important to note that beam attenuation and scattering are not considered as opposed to the dose calculation in this simple approximation. The computed 3D fluence is essentially the dose in air. X-ray generated is approximated from the single radiation source at the X-ray target, and the secondary effective source is not considered. As the mask is not binary in reality, but a function of the aperture size, the fluence for smaller apertures is reduced due to the shadowing of the distributed secondary source by the MLC. Therefore, we note that an approximation to the real mask counterpart is applied in this calculation.
r 0 is the point r projected on the beam portal at 100 cm SAD and couch, gantry and collimator are all at 0°: where R couch , R g , and R col are the couch, gantry, and collimator rotation matrices, respectively, and a, b, and h are the beam couch, gantry, and collimator angles, respectively. P is a 3D-to-2D projection operator that projects a 3D coordinate rðx; y; zÞ to a point r 0 ðu; wÞ within the beam portal according to: where u is oriented along the direction of the X-jaws (or MLC motion), and w is given along the direction of the Y-jaws.
The beam aperture mask M is directly calculated using the jaw and MLC leaf position data. For the projected point r 0 on the beam portal at (u, w), the corresponding leaf pair number can be calculated using w.

The calculation is different for different machine configurations. For a
Varian Millennium 120 MLC module that has 60 MLC leaf pairs, the leaf widths are 1 cm for the first 10 and last 10 leaves, and 0.5 cm for the middle 40 leaves. Leaf pair number L num is calculated from w as: where "int" denotes the integer conversion operation. The point r is considered to be in the beam aperture if u is between the two leaf positions for the relevant leaf pair L num and within the beam opening of the X and Y jaws.
For a DICOM plan, the 3D fluence is calculated similarly as: where k is the control point index and DMU k is the beam MU allocated between control points k and k+1. The rotation angles used in the calculation of r 0 are the averaged values between points k and k + 1. Likewise, the planned source position s is averaged between points k and k + 1 as:

| Implementation details
The number of control points in VMAT plans is usually far less than the number of records in the machine logs. A single 360°arc with a total of 91 control points (4°per control point) within its associated plan will be delivered in 2 min. Over this duration over 5000 log records will be generated. With an angular sampling frequency of 4°p er beam in the plan, the reconstructed 3D fluence volume will have apparent alias; however, the delivery machine linearly interpolates the beam parameters between control points in order to smooth the expected delivered 3D fluence. To calculate the 3D fluence with high accuracy, the control points in the DICOM plans thus need to be up-sampled accordingly. 17 It was empirically determined that 1°p er control point sufficiently reduces alias artifacts.
On the other hand, Varian TrueBeam machines create delivery records every 20 ms with an equivalent angular resolution of 0.048°.
Because such high angular resolution is not necessary for detecting gross delivery errors, machine logs are down-sampled by a factor of 16 to improve computation speed. To combine multiple records into 1 segment, the MLC leaf positions and gantry angles are averaged and the beams MUs are summed.
The reconstruction volumes are automatically determined using the maximal jaw opening from the treatment plan (plus a 1 cm margin) given that the jaw positions are not changing during VMAT delivery. A voxel size of 3 9 3 9 3 mm 3 and 1 degree angular resolution are used in this study in order to provide adequate spatial resolution for error detection with high fidelity and reasonable computation time. QA, which can be described in details as follows:

| 3DFC QA for treatment delivery verification
1. Obtaining the treatment plan and the machine delivery logs.

2.
Calculating the planned and delivered 3D fluences from the DICOM plan delivery logs using the 3D fluence calculation method.

4.
Generating QA reports for physicists' analysis and approval.

5.
Intervening based on failing rates (according to the discretion of a physicist).
A 3% intensity difference and 3%, 3 mm gamma criterion [32][33][34][35] are chosen for defining passing rates based on 3DFC comparisons.   Table 1). The tolerances of beam delivery parameters listed in Table 1 are chosen based on the AAPM Task Group 142 report. 36

| Correlation study design
In order to evaluate the capabilities of the 3DFC QA to detect dose delivery errors, we quantitatively study the correlation between passing rates derived from fluence maps and those observed on dose measurements. Figure 2 (1) and (2), while 3% and 3%, 3 mm are chosen for evaluating differences in (3). The 2% and 2%, 2 mm criteria for (1) and (2) were selected empirically (similarly to the criteria choice for (3), as discussed previously). Furthermore, for (1) and (2), machine systemic errors, e.g., setup errors, are not included. Therefore, tighter constraints with 2%, rather than the 3% difference test and 3%, 3 mm gamma analysis are applied in the first two cases (1) and (2).
Finally, we obtain three groups of resultant passing rates with each group consisting of two test results from both evaluation methods, denoted by P U;IðrÞ and P Φ,c , P DC;IðrÞ and P DC,c , and P Dm;IðrÞ and P DC,c . Five passing rates for each plan from five types of errors are obtained for these three result groups. Both Pearson's and Spearman's correlation coefficients are used to investigate the relationships between groups of passing rates. In particular, r-values (Pearson's correlation coefficient) and q-value (Spearman's correlation coefficients) are calculated to measure the extent to which two variables (e.g., P U;IðrÞ and P DC;IðrÞ ) tend to change together, including both the strength and the direction of the correlation.

| Clinical results
This reported 3DFC QA method has also been applied to QA at the authors' institution for IMRT and VMAT treatments for the

| Lung plan
As lung patients are the most common VMAT-treated patients in our clinic, we present one example of the delivery QA results including both the 3D and 2D fluences, using a four-arc right lung LIU ET AL.

| Simulated delivery error results and analysis
As described in Section 2.5, we first simulated different types of machine errors per control point within normal machine tolerances.
A total number of 10 patients with five lung (4-arc) and five heart (3-arc) VMAT plans were tested for simulated delivery errors. Results of averaged (mean value) failing rates for the 3% intensity fluence difference test and 3%, 3 mm gamma analysis, denoted by F IðrÞ;3% and F c,3%,3mm respectively, are presented in (Table 2). For instance, using the 3DFC method, random gantry angle errors up to 1°could cause mean values of 7.4% and 6.2% of voxels to fail the 3% intensity difference test and 3%, 3 mm gamma analysis, respectively. In contrast, these simulated gantry angle errors were never detected by 2D fluence calculations because gantry angles are not used. Based on these results shown in Table 2, we may therefore conclude that the 3DFC QA method is more sensitive in detecting gantry angle errors, MU errors, jaw position errors, and collimator rotation errors than 2D fluence method.
As also summarized in Table 2, we tested both algorithms upon adding simulated 1-2 mm random MLC errors. We only adjusted the position of leaves that actually contribute to fluence during delivery.
As one can see, both 3D and 2D methods are very sensitive to MLC position errors. However, the results suggest that the 3DFC QA method is less sensitive to MLC positional errors than the 2D method. This might be due to that MLC positional errors only affect the beam fluence at the edges but not inside of beam portals. Arc-CHECK measurements were performed on these unmodified VMAT 3D -axial view 3D -coronal view 3D -sagittal view 2D Results of 3D and 2D fluences from a four-arc lung VMAT plan. Top row is from the DICOM plan. Middle row is from the log file. Bottom row is obtained by calculating the corresponding fluence differences. The PTV contours in the respective 3D orthogonal views are overlaid on the 3D fluences.
test plans. For each plan, the measured dose will be compared with 10 calculated dose files from error-introduced plans (see Section 2.5). Results presented in (   instance, gantry angle errors are scaled to 100% at 1°. As can be seen, failing rates start to climb much more quickly when the errors lie outside their normal machine tolerances. It again demonstrates the conclusion from Table 2 that 3DFC algorithm is more sensitive to MU, jaw position, and collimator rotation errors than 2DFC, while 2DFC cannot catch gantry rotation errors.

| Correlation study results on fluence vs. dose and analysis
In the correlation study, 10 IMRT plans and 10 VMAT plans with five different types of errors were used. Table 3 presents the computed correlations between P U;IðrÞ and P DC;IðrÞ , and between P Φ,c and P DC,c . The described 3DFC method is not designed to catch most errors in treatment planning system, e.g., imperfect beam modeling.
Its primary application is instead to catch certain rare errors such as the junctions of closed MLC leaf pairs left inside the beam field defined by the X and Y jaws in Pinnacle step-and-shoot IMRT plans. 11 Compared to measurement-based QA, the results of 3DFC QA are less independent because the beam parameters in the deliveries were measured by the treatment machines instead by independent measurement device. The beam output and the beam profile are not directly measured, either. The accuracy of the beam parameters provided in the machine log files must be independently verified through routine machine QA in order to be considered reliable. In fact, in one reported incident MLC positions recorded in the log file were shown to be inconsistent with observed, true positions. 37 Therefore, concerns and debates continue on the merits of log-file based QA. 5 For these reasons, the reported 3DFC method is currently used as a complementary tool to measurement-based QA for pre-treatment IMRT and VMAT patient-specific QA in our clinic.
Once confidence has been established via pre-treatment QA derived from calculation and measurement, 3DFC is used to verify the subsequent patient treatment deliveries.
3DFC is also not designed to replace a full dose calculation, but as an alternative approach as a delivery QA with enhanced visualization and error sensitivity, focusing directly on checking machine parameters. Comparing to full 3D dose calculation methods, 3DFC ignores many important physical effects including phantom scattering and attenuation. However, 3DFC is simpler and could be potentially much faster. The current computation speed, 3 to 20 seconds per VMAT beam, accomplished with MATLAB programs could also be significantly improved when 3DFC is reimplemented in C/C++ or GPU programs. It might be worth to note that the computation speed of 3DFC is sufficient for clinical use without GPU acceleration. This allows the reported QA method to be more clinically deployable without the need of relatively expensive GPU hardware. As shown in (Sec- Even though the reported 3DFC method digitally reconstructs 3D fluence from the treatment plan and treatment delivery logs, 3D fluence can be also reconstructed from measured 2D fluence using 2D diode arrays mounted on the gantry and rotate together with the gantry by: where G is a frame of the measured fluence map movie, Dt is the measurement repetition period. Beam MU is not in this equation because it is reflected by the intensity of measured beam fluence. Gantry angles must be simultaneously measured.

| CONCLUSION
An efficient method, 3DFC, has been developed to calculate 3D fluence volumes using the beam parameters from both DICOM plan files and machine delivery log files for verifying both IMRT and VMAT treatment deliveries. This method is designed to work complementarily to other QA procedures including dose recalculations and phantom-based measurements in order to provide a quick and easy measurement of beam delivery fidelity and better visual presentation of delivery errors in 3D. The reported method could be useful in catching both treatment plan data transfer errors and treatment delivery problems.